We discuss the recent achievements in the attractors theory for damped wave equations in bounded domains which are related with Strichartz type estimates. In particular, we present the results related with the well-posedness and asymptotic smoothness of the solution semigroup in the case of critical quintic nonlinearity. The non-autonomous case will be also considered.
 

An important and relevant topic at Thales is 1-3 composite modelling capability. In particular, sensitivity enhancement through design.

A simplistic model developed by Smith and Auld1 has grouped the polycrystalline active and filler materials into an effective homogenous medium by using the rule of weighted averages in order to generate “effective” elastic, electric and piezoelectric properties. This method had been further improved by Avellaneda & Swart2. However, these models fail to provide all of the terms necessary to populate a full elasto-electric matrix – such that the remaining terms need to be estimated by some heuristic approach. The derivation of an approach which allowed all of the terms in the elasto-electric matrix to be calculated would allow much more thorough and powerful predictions – for example allowing lateral modes etc. to be traced and allow a more detailed design of a closely-packed array of 1-3 sensors to be conducted with much higher confidence, accounting for inter-elements coupling which partly governs the key field-of-view of the overall array. In addition, the ability to populate the matrix for single crystal material – which features more independent terms in the elasto-electric matrix than conventional polycrystalline material- would complement the increasing interest in single crystals for practical SONAR devices.

1.“Modelling 1-3 Composite Piezoelectrics: Hydrostatic Response” – IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 40(1):41-

2.“Calculating the performance of 1-3 piezoelectric composites for hydrophone applications: An effective medium approach” The Journal of the Acoustical Society of America 103, 1449, 1998

 The $n$-stranded pure surface braid group of a genus g surface can be described as the subgroup of the pure mapping class group of a surface of genus $g$ with $n$-punctures which becomes trivial on the closed surface. I am interested in the least dilatation of pseudo-Anosov pure surface braids. For the $n=1$ case, upper and lower bounds on the least dilatation were proved by Dowdall and Aougab—Taylor, respectively.  In this talk, I will describe the upper and lower bounds I have proved as a function of $g$ and $n$.

When studying a group, it is natural and often useful to try to cut it up 
onto simpler pieces. Sometimes this can be done in an entirely canonical 
way analogous to the JSJ decomposition of a 3-manifold, in which the 
collection of tori along which the manifold is cut is unique up to isotopy. 
It is a theorem of Brian Bowditch that if the group acts nicely on a metric 
space with a negative curvature property then a canonical decomposition can 
be read directly from the large-scale geometry of that space. In this talk 
we shall explore an algorithmic consequence of this relationship between 
the large-scale geometry of the group and is algebraic decomposition.

Ultrasound (US) imaging is one of the first steps in a continuum of pregnancy care. During the fetal period, the brain undergoes dramatic structural changes, many of which are informative of healthy maturation. The resolution of modern US machines enables us to observe and measure brain structures, as well as detect cerebral abnormalities in fetuses from as early as 18 weeks. Recent breakthroughs in machine learning techniques for image analysis introduce opportunities to  develop bespoke methods to track spatial and temporal patterns of fetal brain development. My work focuses on the design of appropriate data-driven techniques to extract developmental information from standard clinical US images of the brain.

In this talk, I will review a number of interdisciplinary collaborations in which I have been involved over the years that have coupled mathematical
modelling with experimental studies to try to advance our understanding of processes in biology and medicine. Examples will include somatic evolution in
tumours, collective cell movement in epithelial sheets, cell invasion in neural crest, and pattern formation in slime mold. These are examples where
verbal reasoning models are misleading and insufficient, while mathematical models can enhance our intuition.

Please note that this will be held at Tsuzuki Lecture Theatre, St Annes College, Oxford.

Please note that you will need to register for this event via https://www.eventbrite.co.uk/e/qbiox-colloquium-trinity-term-2018-ticke…

ATP-sensitive potassium (KATP) channels are critical for coupling changes in blood glucose to insulin secretion. Gain-of-function mutations in KATP channels cause a rare inherited form of diabetes that manifest soon after birth (neonatal diabetes). This talk shows how understanding KATP channel function has enabled many neonatal diabetes patients to switch from insulin injections to sulphonylurea drugs that block KATP channel activity, with considerable improvement in their clinical condition and quality of life.   Using a mouse model of neonatal diabetes, we also found that as little as 2 weeks of diabetes led to dramatic changes in gene expression, protein levels and metabolite concentrations. This reduced glucose-stimulated ATP production and insulin release. It also caused substantial glycogen storage and β-cell apoptosis. This may help explain why older neonatal diabetes patients with find it more difficult to transfer to drug therapy, and why the drug dose decreases with time in many patients. It also suggests that altered metabolism may underlie both the progressive impairment of insulin secretion and reduced β-cell mass in type 2 diabetes.

I will discuss some properties of delay differential equations in which the delay is not prescribed a-priori but is determined from a threshold condition. Sometimes the delay depends on the solution of the differential equation and its history. A scenario giving rise to a threshold type delay is that larval insects sometimes experience halting or slowing down of development, known as diapause, perhaps as a consequence of intra-specific competition among larvae at higher densities. Threshold delays can result in population dynamical models having some unusual properties, for example, if the model has an Allee effect then diapause may cause extinction in some parameter regimes even where the initial population is high.

Please  note that this talk is only suitable for Mathematicians.